Answer:
Paying the $20,000 in December is the clear winner. Accelerating her payment from January to December will increase the present value of the cash outflow by a few days. Thus, there is a minor present value cost associated with accelerating her payment.
Explanation:
Option 1: Pay $20,000 bill in December:
$20,000 tax deduction x 40% marginal tax rate = $8,000 in present value tax savings
After-tax cost = Pretax cost - Present Value Tax Savings
= $20,000 - $8,000 = $12,000
Option 2: Pay $20,000 bill in January:
$20,000 x 40% = $8,000
Present Value of Tax savings = $8,000 x .893 (Discount factor, 1 year, 12%) = $7, 144
After-tax cost = Pretax cost - Present value tax savings
= $20,000 - $7,144 = $12,856
